Dear All,
University of Warsaw, Faculty of Philosophy is offering two post-doc positions (14 months and 24 months) to work within the project “Logical and Epistemological Criteria of Salience in the Foundations of Mathematics”. The deadline for the submissions is the 31st of August.
Within the project we study formal and epistemological criteria which can provide a principled way of filtering out “natural” or “salient” mathematical theories from the artificial ones. Intuitively speaking, a “natural” mathematical theory is one, which “grasps” an important mathematical notion (such as a set or a number) in a sufficiently precise way or can be associated with a well-motivated standpoint in the philosophy of mathematics (such as finitism or predicativism). The examples of natural theories are Peano Arithmetic (PA), Zermelo-Frankel set theory (ZF) or Primitive Recursive Arithmetic (PRA).
In the project we approach the above problem from three different angles
- We study formal properties of theories which are inspired by the notion of categoricity, such as internal categoricity, solidity, tightness and we aim at providing the philosophical analysis of the formal results. A good example of this kind of research is given in the paper “Categoricity-like properties in the first-order realm” (https://doi.org/10.36253/jpm-2934).
- We analyze the notion of epistemic stability in the sense of “Arithmetical Reflection and the Provability of Soundness” (https://doi.org/10.1093/philmat/nku026)
- We study language-independent characterizations of axiomatic theories up to a suitable interpretability notion, in the spirit of “Universal Properties of Truth” (https://doi.org/10.1142/S0219061324500314).
A more detailed description of the project can be found in:
https://sites.google.com/uw.edu.pl/lelyk/projects 
Full information about the appointment conditions and the recruitment procedure can be found at Euraxess
https://euraxess.ec.europa.eu/jobs/364335 (24 months)
https://euraxess.ec.europa.eu/jobs/364392 (14 months)